A004332 a(n) = C(4n,n-2).

1, 12, 120, 1140, 10626, 98280, 906192, 8347680, 76904685, 708930508, 6540715896, 60403728840, 558383307300, 5166863427600, 47855699958816, 443643407165376, 4116305022165108, 38223742100828400, 355214207837288800

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A002293.

Programs

Mathematica

Table[Binomial[4n,n-2],{n,2,20}]  (* Harvey P. Dale, Apr 11 2011 *)

PARI

a(n) = binomial(4*n,n-2); \\ Michel Marcus, May 10 2020

Formula

G.f.: g*(g-1)^2/(4-3*g) where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 17 2011

-3*(3*n+2)*(n-2)*(3*n+1)*a(n) + 8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1) = 0. - R. J. Mathar, May 27 2014